Unstructured spline spaces for isogeometric analysis based on spline manifolds

• DOI: 10.1016/j.cagd.2016.05.004
• Publication Date: 2016-05-28T15:01:08Z
• Authors: Giancarlo Sangalli; Thomas Takacs; Rafael Vázquez
• Keywords: Multi-patch; Spline manifold; Unstructured T-spline; Aerospace Engineering; Unstructured T-splines; Numerical Analysis (math.NA); 02 engineering and technology; Computer Graphics and Computer-Aided Design; Isogeometric analysis; Modeling and Simulation; Automotive Engineering; FOS: Mathematics; 0202 electrical engineering, electronic engineering, information engineering; Mathematics - Numerical Analysis; Isogeometric analysi

Based on spline manifolds we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces that have a tensor-product structure locally, but not globally. This includes configurations such as B-splines over multi-patch domains with extraordinary points, analysis-suitable unstructured T-splines, or more general constructions. Within this framework, we generalize the concept of dual-compatible B-splines, which was originally developed for structured T-splines. This allows us to prove the key properties that are needed for isogeometric analysis, such as linear independence and optimal approximation properties for $h$-refined meshes.